Fifteenth
Encyclopedia
In music
, a fifteenth or double octave, abbreviated 15ma, is the interval
between one musical note
and another with one-quarter the wavelength
or quadruple the frequency
. The fourth harmonic, it is two octave
s. It is referred to as a fifteenth because, in the diatonic scale, there are 15 notes between them if one counts both ends (as is customary). Two octaves (based on the Italian
word for eighth) do not make a sixteenth, but a fifteenth. In other contexts, the term two octaves is likely to be used.
For example, if one note has a frequency of 400 Hz
, the note a fifteenth above it is at 1600 Hz (15ma ), and the note a fifteenth below is at 100 Hz (15mb ). The ratio of frequencies of two notes a fifteenth apart is therefore 4:1.
As the fifteenth is a multiple of octaves, the human ear
tends to hear
both notes as being essentially "the same", as it does the octave. Like the octave, in the Western system of music notation
notes a fifteenth apart are given the same name—the name of a note an octave above A is also A. However, because of the large frequency distance between the notes, it is less likely than an octave to be judged the same pitch by non-musicians. Passages in parallel fifteenths are much less common than parallel octaves. In particular, sometimes an organist will use two stops
a fifteenth away (notated as 2′).
Like the notation 8va for octave
, 15ma means "play two octaves higher than written." It could also mean two octaves lower, but that is usually notated 15mb. Either direction can be cancelled with the word loco, but often a dashed line or bracket indicates the extent of the music affected.
The notations 16va and 16vb are sometimes mistakenly used instead.
Music
Music is an art form whose medium is sound and silence. Its common elements are pitch , rhythm , dynamics, and the sonic qualities of timbre and texture...
, a fifteenth or double octave, abbreviated 15ma, is the interval
Interval (music)
In music theory, an interval is a combination of two notes, or the ratio between their frequencies. Two-note combinations are also called dyads...
between one musical note
Note
In music, the term note has two primary meanings:#A sign used in musical notation to represent the relative duration and pitch of a sound;#A pitched sound itself....
and another with one-quarter the wavelength
Wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...
or quadruple the frequency
Frequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...
. The fourth harmonic, it is two octave
Octave
In music, an octave is the interval between one musical pitch and another with half or double its frequency. The octave relationship is a natural phenomenon that has been referred to as the "basic miracle of music", the use of which is "common in most musical systems"...
s. It is referred to as a fifteenth because, in the diatonic scale, there are 15 notes between them if one counts both ends (as is customary). Two octaves (based on the Italian
Italian language
Italian is a Romance language spoken mainly in Europe: Italy, Switzerland, San Marino, Vatican City, by minorities in Malta, Monaco, Croatia, Slovenia, France, Libya, Eritrea, and Somalia, and by immigrant communities in the Americas and Australia...
word for eighth) do not make a sixteenth, but a fifteenth. In other contexts, the term two octaves is likely to be used.
For example, if one note has a frequency of 400 Hz
Hertz
The hertz is the SI unit of frequency defined as the number of cycles per second of a periodic phenomenon. One of its most common uses is the description of the sine wave, particularly those used in radio and audio applications....
, the note a fifteenth above it is at 1600 Hz (15ma ), and the note a fifteenth below is at 100 Hz (15mb ). The ratio of frequencies of two notes a fifteenth apart is therefore 4:1.
Ear
The ear is the organ that detects sound. It not only receives sound, but also aids in balance and body position. The ear is part of the auditory system....
tends to hear
Hearing (sense)
Hearing is the ability to perceive sound by detecting vibrations through an organ such as the ear. It is one of the traditional five senses...
both notes as being essentially "the same", as it does the octave. Like the octave, in the Western system of music notation
Musical notation
Music notation or musical notation is any system that represents aurally perceived music, through the use of written symbols.-History:...
notes a fifteenth apart are given the same name—the name of a note an octave above A is also A. However, because of the large frequency distance between the notes, it is less likely than an octave to be judged the same pitch by non-musicians. Passages in parallel fifteenths are much less common than parallel octaves. In particular, sometimes an organist will use two stops
Organ stop
An organ stop is a component of a pipe organ that admits pressurized air to a set of organ pipes. Its name comes from the fact that stops can be used selectively by the organist; some can be "on" , while others can be "off" .The term can also refer...
a fifteenth away (notated as 2′).
Like the notation 8va for octave
Octave
In music, an octave is the interval between one musical pitch and another with half or double its frequency. The octave relationship is a natural phenomenon that has been referred to as the "basic miracle of music", the use of which is "common in most musical systems"...
, 15ma means "play two octaves higher than written." It could also mean two octaves lower, but that is usually notated 15mb. Either direction can be cancelled with the word loco, but often a dashed line or bracket indicates the extent of the music affected.
The notations 16va and 16vb are sometimes mistakenly used instead.